Networks rise in several aspects of modern life, motivating us to model and understand them. Several types of mathematical and algorithmic problems arise in networks. Opinion dynamics is a process in networks modelling the effect of local interactions on agents’ beliefs. The beliefs can be thought as a belief for some common question of interest, for instance the probability of some event. In this thesis, I will present mathematical models which capture such processes in networks and state mathematical problems on them. I try to evaluate these pro- cesses in terms of economic behavior and convergence time of dynamic processes. We would ideally like to connect these quantities with parameters of the network structure. Finally, motivated by polls present on political elections, we study the effect of partial global information on agents’ local interactions and behavior.